---
_id: '46393'
abstract:
- lang: eng
  text: In multi-objective optimization, set-based performance indicators have become
    the state of the art for assessing the quality of Pareto front approximations.
    As a consequence, they are also more and more used within the design of multi-objective
    optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two
    popular examples. In order to understand the behavior and the approximations preferred
    by these indicators and algorithms, a comprehensive knowledge of the indicator’s
    properties is required. Whereas this knowledge is available for the HV, we presented
    a first approach in this direction for the R2 indicator just recently. In this
    paper, we build upon this knowledge and enhance the considerations with respect
    to the integration of preferences into the R2 indicator. More specifically, we
    analyze the effect of the reference point, the domain of the weights, and the
    distribution of weight vectors on the optimization of $\mu$ solutions with respect
    to the R2 indicator. By means of theoretical findings and empirical evidence,
    we show the potentials of these three possibilities using the optimal distribution
    of $\mu$ solutions for exemplary setups.
author:
- first_name: Tobias
  full_name: Wagner, Tobias
  last_name: Wagner
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Dimo
  full_name: Brockhoff, Dimo
  last_name: Brockhoff
citation:
  ama: 'Wagner T, Trautmann H, Brockhoff D. Preference Articulation by Means of the
    R2 Indicator. In: Purshouse RC, Fleming PJ, Fonseca CM, Greco S, Shaw J, eds.
    <i>Evolutionary Multi-Criterion Optimization</i>. Springer Berlin Heidelberg;
    2013:81–95.'
  apa: Wagner, T., Trautmann, H., &#38; Brockhoff, D. (2013). Preference Articulation
    by Means of the R2 Indicator. In R. C. Purshouse, P. J. Fleming, C. M. Fonseca,
    S. Greco, &#38; J. Shaw (Eds.), <i>Evolutionary Multi-Criterion Optimization</i>
    (pp. 81–95). Springer Berlin Heidelberg.
  bibtex: '@inproceedings{Wagner_Trautmann_Brockhoff_2013, place={Berlin, Heidelberg},
    title={Preference Articulation by Means of the R2 Indicator}, booktitle={Evolutionary
    Multi-Criterion Optimization}, publisher={Springer Berlin Heidelberg}, author={Wagner,
    Tobias and Trautmann, Heike and Brockhoff, Dimo}, editor={Purshouse, Robin C.
    and Fleming, Peter J. and Fonseca, Carlos M. and Greco, Salvatore and Shaw, Jane},
    year={2013}, pages={81–95} }'
  chicago: 'Wagner, Tobias, Heike Trautmann, and Dimo Brockhoff. “Preference Articulation
    by Means of the R2 Indicator.” In <i>Evolutionary Multi-Criterion Optimization</i>,
    edited by Robin C. Purshouse, Peter J. Fleming, Carlos M. Fonseca, Salvatore Greco,
    and Jane Shaw, 81–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.'
  ieee: T. Wagner, H. Trautmann, and D. Brockhoff, “Preference Articulation by Means
    of the R2 Indicator,” in <i>Evolutionary Multi-Criterion Optimization</i>, 2013,
    pp. 81–95.
  mla: Wagner, Tobias, et al. “Preference Articulation by Means of the R2 Indicator.”
    <i>Evolutionary Multi-Criterion Optimization</i>, edited by Robin C. Purshouse
    et al., Springer Berlin Heidelberg, 2013, pp. 81–95.
  short: 'T. Wagner, H. Trautmann, D. Brockhoff, in: R.C. Purshouse, P.J. Fleming,
    C.M. Fonseca, S. Greco, J. Shaw (Eds.), Evolutionary Multi-Criterion Optimization,
    Springer Berlin Heidelberg, Berlin, Heidelberg, 2013, pp. 81–95.'
date_created: 2023-08-04T15:47:49Z
date_updated: 2023-10-16T13:47:58Z
department:
- _id: '34'
- _id: '819'
editor:
- first_name: Robin C.
  full_name: Purshouse, Robin C.
  last_name: Purshouse
- first_name: Peter J.
  full_name: Fleming, Peter J.
  last_name: Fleming
- first_name: Carlos M.
  full_name: Fonseca, Carlos M.
  last_name: Fonseca
- first_name: Salvatore
  full_name: Greco, Salvatore
  last_name: Greco
- first_name: Jane
  full_name: Shaw, Jane
  last_name: Shaw
language:
- iso: eng
page: 81–95
place: Berlin, Heidelberg
publication: Evolutionary Multi-Criterion Optimization
publication_identifier:
  isbn:
  - 978-3-642-37140-0
publisher: Springer Berlin Heidelberg
status: public
title: Preference Articulation by Means of the R2 Indicator
type: conference
user_id: '15504'
year: '2013'
...